A school is planning a field trip for 142 people. the trip will use six drivers and two types of vehicles : buses and vans. A bus can seat 51 passngers.

Question

A van can seat 10 passengers. Write and solve a system of equations to find how many buses and how many vans will be needed

Answer 1

six vehicles, buses and vans:

b + v = 6

b = 6 - v

 

Question:  Are the drivers included in the 142 total

persons?

 

51b + 10v = 142

51(6-v) + 10v = 142

316 - 51v + 10v = 142

-41v = 142-316

-41v = -174

v = 4.2439

b = 1.7561

 

2 buses and 4 vans:  2(52)+4(11) = 148 person

capacity: 142 attendees and 6 drivers.

 

Note: each bus holds 52 persons ...

51 passengers and the driver.

Each van holds 11 persons by same logic.. 10+driver